Question

Find the $\sqrt{(1+\frac{27}{169})}=(1+\frac{x}{13})$

Answer 1

$\sqrt{1+\frac{27}{169}}=1+\frac{x}{13}$

$\Rightarrow 1+\frac{27}{169}={(1+\frac{x}{13})}^2$

$\Rightarrow 1+\frac{27}{169}=1+\frac{x^2}{169}+\frac{2x}{13}$

$\Rightarrow x^2+26x-27=0$

$\Rightarrow x^2+27x-x-27=0$

$\Rightarrow x(x+27)-1(x+27)=0$

So $x=-27$ or $x=1$

Since $x=-27$ is not possible.

Hence $x=1$.